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Modified tests for a change in persistence

  • Harvey, David I.
  • Leybourne, Stephen J.
  • Taylor, A.M. Robert

Being able to correctly characterise an observed time series into its separate difference stationary and trend stationary regimes, should they exist, has important implications for effective model building and forecasting in economics and finance. Existing ratio-based statistics test the null hypothesis that a time series displays constant trend stationarity, I(0), against the alternative of a change in persistence from trend stationarity to difference stationarity, I(1), or vice versa. Here, however, we demonstrate that these tests are unable to adequately discern between a true change in persistence and a constant I(1) process. We propose modified tests which, by design, have the same critical values regardless of whether the process is I(0) or I(1) throughout. Hence, our null hypothesis is that of constant persistence (either constant I(0) or constant I(1)). Tests directed against both I(1) to I(0) and I(0) to I(1) persistence changes are provided, together with tests where the direction of change under the alternative is unspecified. Our tests retain the same rates of consistency against persistence change processes as their unmodified counterparts. Simulation evidence suggests that our new procedures work extremely well in practice, with the modified tests correctly being sized in both constant I(0) and constant I(1) environments, and displaying only very modest losses in power, relative to unmodified tests, against persistence change process

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 134 (2006)
Issue (Month): 2 (October)
Pages: 441-469

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Handle: RePEc:eee:econom:v:134:y:2006:i:2:p:441-469
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Kim, Jae-Young & Belaire-Franch, Jorge & Amador, Rosa Badillo, 2002. "Corrigendum to "Detection of change in persistence of a linear time series" [J. Econom. 95 (2000) 97-116]," Journal of Econometrics, Elsevier, vol. 109(2), pages 389-392, August.
  2. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  3. Emery, Kenneth M., 1994. "Inflation persistence and Fisher effects: Evidence of a regime change," Journal of Economics and Business, Elsevier, vol. 46(3), pages 141-152, August.
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  5. Busetti, Fabio & Taylor, A. M. Robert, 2004. "Tests of stationarity against a change in persistence," Journal of Econometrics, Elsevier, vol. 123(1), pages 33-66, November.
  6. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  7. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  8. Stephen Leybourne & Tae-Hwan Kim & Vanessa Smith & Paul Newbold, 2003. "Tests for a change in persistence against the null of difference-stationarity," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 291-311, December.
  9. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  10. Clarida, R. & Gali, J. & Gertler, M., 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and some Theory," Working Papers 98-01, C.V. Starr Center for Applied Economics, New York University.
  11. Anindya Banerjee & Robin L. Lumsdaine & James H. Stock, 1990. "Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence," NBER Working Papers 3510, National Bureau of Economic Research, Inc.
  12. Vogelsang, Timothy J, 1998. "Testing for a Shift in Mean without Having to Estimate Serial-Correlation Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 73-80, January.
  13. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
  14. Ozgen Sayginsoy, 2005. "Powerful and Serial Correlation Robust Tests of the Economic Convergence Hypothesis," Econometrics 0503014, EconWPA, revised 11 Mar 2005.
  15. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  16. Kim, Jae-Young, 2000. "Detection of change in persistence of a linear time series," Journal of Econometrics, Elsevier, vol. 95(1), pages 97-116, March.
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